Just keep in mind LiFePO4 doesn't tolerate charging below freezing, so if you plan to use it in freezing temps it would be better to locate the battery inside the vehicle. This would probably require using a supercapacitor bank in the engine bay to provide the CCA the starter motor needs. You could downsize your battery if you go with a LiFePO4 and super capacitor bank. What is the electrical draw while the engine is off?

The weight reduction would be nice as this car is already quite light at 845 kg.

As oil pan says, this is likely more hassle than it's worth considering the temperature sensitivity.

If I were to tackle this project I'd start by measuring typical electrical draw while the engine is off. This would determine what size battery to run, but I wouldn't go less than 20 Ah. I always recommend this 20 Ah pack:

You would connect the cabin located LiFePO4 in parallel to the caps that live in the engine bay, possibly with a very low ohm current limiting resistor. The resistor would force the caps to do the majority of the heavy lifting to prevent the wires and LiFePO4 from overcurrent.

Remember I have been using LiFePO4 starting batteries since 2010, I live in new Mexico which has pretty mild winters and I know all about their cold sensitivity.
If someone in a cold climate switches over to them, learns everything the hard way they will be very disappointed and switch back to lead acid with in a year.

The battery has to be located away from engine heat, which means most people will have to relocate it and needs to be brought inside at night when the temperature drops down near freezing.

I don't think they are more hassle than they are worth but I was prepared to relocate the battery and bring it in on frosty nights.
The batteries have lasted far longer than any lead acid, but I take real good care of them.

Any reason to be concerned that the OEM alternator was not designed for lithium? I understand such smart alternators will deliver voltage that is incorrect. I imagine if you kept the alt off most of the time and charger from the grid through a proper charger, using alt only as a range extender, one could get better life/service out of a lithium.

I don't think they are more hassle than they are worth but I was prepared to relocate the battery and bring it in on frosty nights.
The batteries have lasted far longer than any lead acid, but I take real good care of them.

I'm on year 3 of running one in the Prius. The battery was already located in the cabin, so it was simple to replace. I don't bring it in when it's freezing and take no special precautions to protect it. Since the Prius doesn't use the battery to start the engine, the loads are relatively low. No supercap required.